数学
数学优化
切锥
集合(抽象数据类型)
订单(交换)
功能(生物学)
切线
正多边形
对偶(序理论)
可行区
最优化问题
计算机科学
组合数学
生物
进化生物学
经济
财务
程序设计语言
几何学
作者
Helmut Gfrerer,Jane J. Ye,Jinchuan Zhou
标识
DOI:10.1287/moor.2021.1211
摘要
In this paper, we study second-order optimality conditions for nonconvex set-constrained optimization problems. For a convex set-constrained optimization problem, it is well known that second-order optimality conditions involve the support function of the second-order tangent set. In this paper, we propose two approaches for establishing second-order optimality conditions for the nonconvex case. In the first approach, we extend the concept of the support function so that it is applicable to general nonconvex set-constrained problems, whereas in the second approach, we introduce the notion of the directional regular tangent cone and apply classical results of convex duality theory. Besides the second-order optimality conditions, the novelty of our approach lies in the systematic introduction and use, respectively, of directional versions of well-known concepts from variational analysis.
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